forensim (version 2.0)

RMP: The Random Match Probability of DNA evidence (RMP)

Description

RMP computes the random match probability of DNA evidence given in a matrix (or data frame) or in a text file. Several situations are handled: the suspect and an unknown offender are unrelated, or are members of the same subpopulation with a given coancestry coefficient theta, or are close relatives. For the latter case, the relationship is described by the kinship coefficients.

Usage

RMP(suspect=NULL, filename=NULL, freq, k=c(1,0,0), theta=0,refpop=NULL)

Arguments

suspect

a matrix or a data frame of dimension L x 2, L being the number of loci involved in the DNA evidence. The first column gives the loci names, and the second column gives the suspect's genotype at each locus. A genotype is coded as a character where ea

filename

the file name from which the input data should be read. Data mut be a matrix of dimension L x 2, L being the number of loci involved in the DNA evidence.The first column gives the loci names, and the second column gives the suspect's genotype at each

freq

a tabfreq object giving the allele frequencies

k

vector of kinship coefficients (k0, k1, k2), where ki is the probability that two people (the suspect and an unknown offender) will share i alleles identical by descent, i = 0, 1, 2.

theta

a float in [0,1[. theta is equivalent to Wright's Fst. In case of population subdivision, it allows a correction of the allele frequencies in the subpopulation of interest

refpop

the reference population in freq from which to extract the allele frequencies fro the RMP calculation. This argument is obligatory only if freq contains allele frequencies from several populations

Value

• RMP returns a list with the following components:
• RMP.loc
  single-locus match probabilities
• RMP
  multiloci match probability (product of single-locus match probabilities)

Details

The match probability is derived from Balding and Nichols (1994) and is computed as: $$k_2 + k_1 Z_1 + k_0 Z_2$$ where $k_0, k_1, k_2$ are the kinship coefficients, $Z_1$ is the match probability when the suspect an the unknown offender share one allele identical-by-descent. $Z_2$ is the match probability in the unrelated case, when the suspect an the unknown offender share 0 allele identical-by-descent. In the homozygous case, with the allele frequency $p_i$: $$Z_1=\frac{2\theta + (1-\theta)p_i}{1+\theta}$$ $$Z_2=\frac{\left[2\theta+(1-\theta)p_i\right] \left[3\theta+(1-\theta)p_i \right]}{(1+\theta)(1+2\theta)}$$ In the heterozygous case, with allele frequencies $p_i$ and $p_j$: $$Z_1=\frac{2\theta + (1-\theta)(p_i+p_j)}{2(1+\theta)}$$ $$Z_2=\frac{2\left[\theta+(1-\theta)p_i\right] \left[\theta+(1-\theta)p_j \right]}{(1+\theta)(1+2\theta)}$$ $\theta$ is Wright's Fst coefficient, usually called the coancestry coefficient in forensic studies. Main effects of allele dependencies between loci in the suspect's subpopulation are taken into account though the coancestry coefficient, hence, the match probability at all loci is, to a close approximation, the product of single-locus probabilities.

References

Balding DJ, Nichols RA. DNA profile match probability calculation: How to allow for population stratification, relatedness, database selection and single bands. Forensic Sci I 1994;64:125-140.

See Also

LR for the evaluation of DNA evidence through likelihood ratio

Examples

# random match probability 
# data input 

data <- matrix(c("CSF1PO","FGA","TH01","TPOX","VWA","D3S1358","D5S818",
"D7S820","D8S1179","D13S317","D16S539","D18S51","D21S11","D2S1338","D19S433",
"12/11","22/19","6/7","10/8","17/18","18/17","12/12","8/8","13/13","11/11",
"12/10","14/15","33.2/32.2","23/22","14/14"),nc=2)
colnames(data)<- c('locus','genotype')
#15-locus genotype
data
#allele frequencies are taken from the strusa data set

data(strusa)

RMP(suspect=data,freq=strusa,refpop="Cauc")

# using a preexisting file from the forensim package
RMP(filename=system.file("files/exprofile.txt", package = "forensim"),
freq=strusa,refpop="Cauc")